Yes, the military draft is just, if there are not adequate volunteers to go to war. A person who lives in a country should have the protections of the country, but at the same time, they have an obligation to go to war and defend the freedoms of the country if they need to.
I know SCOTUS ruled in Arver that conscription wasn't slavery or involuntary servitude. However the reasoning they used amounted to "it doesn't count because in this case it's good." If we use that as a definition for anything prohibited in the Constitution then the Constitution becomes entirely arbitrary.
I think that generally military service should be voluntary and if not then mild means such as fines rather than jail time should be used to coerce people to join. If push comes to shove then we should do it properly and amend the Constitution.
If we keep just going ahead and ignoring the Constitution and making ridiculous arguments to justify it then the Constitution won't mean anything. If it is necessary to stray from the Constitution we shouldn't use arguments to try to get around it or avoid it instead we should do it properly and amend it.
The military draft forces people to stand up for a cause and fight for a country or looked like cowards for dodging it. The patriotic stance is forced upon an individual and they lose their freedom of liberty in being subjected to participate in a war they did not commission or warrant. If the country is fighting a war in which the people stand firm in agreement with, then there will be many who sign up. If the war is more opposed to than anything, then the people shouldn't have to endure the atrocities the nation wishes to put upon them. Many were born into this country and appreciate it, but should not be forced to die because of it.